Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound

Xiaoqiang Wang; Xun Song; Dabin Zheng; Hao Chen; Cunsheng Ding

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arXiv · 2606.02262

Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound

Xiaoqiang Wang·Xun Song·Dabin Zheng·Hao Chen·Cunsheng Ding

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Abstract

In spite of the intensive study of cyclic codes and the recent construction of an infinite family of self-dual binary cyclic codes whose minimum distances have the square-root bound in IEEE Trans. IT, vol. 71, no. 4, 2025, it is still a 70-year-old open problem whether there is an infinite family of self-dual binary cyclic codes whose minimum distances have a lower bound better than the square-root bound. This paper settles this long-standing open problem in coding theory by presenting infinite families of such self-dual binary cyclic codes. As by-products, several families of cyclic codes with better parameters than those in some references are also constructed in this paper.

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Xiaoqiang Wang, Xun Song, Dabin Zheng, Hao Chen, Cunsheng Ding. 2026-06-01. Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound. https://arxiv.org/abs/2606.02262

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